Efficient Low Order Virtual Elements for Anisotropic Materials at Finite Strains

authored by: P. Wriggers, B. Hudobivnik, J. Korelc
Abstract: Virtual elements were introduced in the last decade and applied to problems in solid mechanics. The success of this methodology when applied to linear problems asks for an extension to the nonlinear regime. This work is concerned with the numerical simulation of structures made of anisotropic material undergoing large deformations. Especially problems with hyperelastic matrix materials and transversly isotropic behaviour will be investigated. The virtual element formulation is based on a low-order formulations for problems in two dimensions. The elements can be arbitrary polygons. The formulation considered relies on minimization of energy, with a novel construction of the stabilization energy and a mixed approximation for the fibers describing the anisotropic behaviour. The formulation is investigated through a several numerical examples, which demonstrate their efficiency, robustness, convergence properties, and locking-free behaviour.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Ljubljana
Type: Contribution to book/anthology
Pages: 417-434
No. of pages: 18
Publication date: 10.09.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Modelling and Simulation, Biomedical Engineering, Computer Science Applications, Fluid Flow and Transfer Processes, Computational Mathematics, Electrical and Electronic Engineering
Electronic version(s): https://doi.org/10.1007/978-3-319-60885-3_20 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@inbook{db50e0ab3b2d44ccb59ae322f1795a70,
title = "Efficient Low Order Virtual Elements for Anisotropic Materials at Finite Strains",
abstract = "Virtual elements were introduced in the last decade and applied to problems in solid mechanics. The success of this methodology when applied to linear problems asks for an extension to the nonlinear regime. This work is concerned with the numerical simulation of structures made of anisotropic material undergoing large deformations. Especially problems with hyperelastic matrix materials and transversly isotropic behaviour will be investigated. The virtual element formulation is based on a low-order formulations for problems in two dimensions. The elements can be arbitrary polygons. The formulation considered relies on minimization of energy, with a novel construction of the stabilization energy and a mixed approximation for the fibers describing the anisotropic behaviour. The formulation is investigated through a several numerical examples, which demonstrate their efficiency, robustness, convergence properties, and locking-free behaviour.",
author = "P. Wriggers and B. Hudobivnik and J. Korelc",
note = "Funding information: The paper is a contribution to honor Professor Roger Owen on behalf of his 75th birthday. The authors like to thank Roger Owen for his continuous support and friendship throughout the last four decades of research on finite element methods. The first author would like to thank for the support of the DFG within the priority program SPP 1748 1748 {\textquoteleft}Reliable simulation techniques in solid mechanics: Development of non-standard discretization methods, mechanical and mathematical analysis{\textquoteright} under the project WR 19/50-1.",
year = "2017",
month = sep,
day = "10",
doi = "10.1007/978-3-319-60885-3_20",
language = "English",
series = "Computational Methods in Applied Sciences",
publisher = "Springer Basel AG",
pages = "417--434",
booktitle = "Advances in Computational Plasticity",
address = "Switzerland",
}